Editing Clairaut's theorem (gravity) (section)

{{short description|Theorem about gravity}}
{{other uses|Clairaut's formula (disambiguation)}}
[[File:Elipsoid zplostely.png|thumb|200px |Figure 1: An ellipsoid]]
[[File:Gnuplot ellipsoid.svg|thumb|200px|Figure 2: Wireframe rendering of an ellipsoid (oblate spheroid)]]

'''Clairaut's theorem''' characterizes the surface gravity on a viscous rotating [[ellipsoid]] in [[hydrostatic equilibrium]] under the action of its gravitational field and centrifugal force.  It was published in 1743 by [[Alexis Clairaut|Alexis Claude Clairaut]] in a treatise<ref name=RoyalSoc>''Théorie de la figure de la terre, tirée des principes de l'hydrostatique'' (''Theory of the shape of the earth, drawn from the principles of hydrostatics'') [https://archive.org/details/cataloguescient01librgoog/page/n144 <!-- pg=134 quote="Théorie de la figure de la terre". --> From the catalogue of the scientific books in the library of the Royal Society.]</ref> which synthesized physical and geodetic evidence that the Earth is an oblate rotational [[ellipsoid]].<ref name= Torge>{{cite book |title=Geodesy: An Introduction |edition=3rd |author=Wolfgang Torge |page=10 |url=https://books.google.com/books?id=pFO6VB_czRYC&dq=%22Clairaut%27s+theorem%22&pg=PA10 |isbn=3-11-017072-8 |year=2001 |publisher=[[Walter de Gruyter]]   }}</ref><ref name=Routh>{{cite book |author=Edward John Routh |title=A Treatise on Analytical Statics with Numerous Examples |page=154  |year=2001|isbn=1-4021-7320-2 |publisher=Adamant Media Corporation |volume=2 |url=https://books.google.com/books?id=yKmdk4LZxhMC&pg=PA154 }} A reprint of the original work published in 1908 by Cambridge University Press.</ref> It was initially used to relate the gravity at any point on the Earth's surface to the position of that point, allowing the [[ellipticity]] of the Earth to be calculated from measurements of gravity at different latitudes.  Today it has been largely supplanted by the [[Somigliana equation]].